Question: Solve for $x$ and $y$ using substitution. ${-5x-y = -8}$ ${y = -2x+5}$
Explanation: Since $y$ has already been solved for, substitute $-2x+5$ for $y$ in the first equation. ${-5x - }{(-2x+5)}{= -8}$ Simplify and solve for $x$ $-5x+2x - 5 = -8$ $-3x-5 = -8$ $-3x-5{+5} = -8{+5}$ $-3x = -3$ $\dfrac{-3x}{{-3}} = \dfrac{-3}{{-3}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {y = -2x+5}\thinspace$ to find $y$ ${y = -2}{(1)}{ + 5}$ $y = -2 + 5$ $y = 3$ You can also plug ${x = 1}$ into $\thinspace {-5x-y = -8}\thinspace$ and get the same answer for $y$ : ${-5}{(1)}{ - y = -8}$ ${y = 3}$